Subgroups — C₂²×C₃³×C₄×C₂₉ #72190877

Order 12528.

1512 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×C₄×C₂₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃²×C₄×C₂₉	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³×C₂₉	C₄	1	4	yes	direct product factor
5	C₂²×C₃³×C₂₉	C₂²	1	3	yes	—
6	C₃³×C₄×C₂₉	C₂²	1	4	yes	direct product factor
7	C₂³×C₃²×C₂₉	C₂×C₃	1	13	yes	—
8	C₂×C₃²×C₄×C₂₉	C₂×C₃	1	78	yes	direct product factor
9	C₂×C₃³×C₂₉	C₂×C₄	1	6	yes	direct product factor
10	C₂×C₃³×C₂₉	C₂³	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₂₉	C₃²	1	13	yes	direct product factor
12	C₂²×C₃²×C₂₉	C₃×C₄	1	52	yes	direct product factor
13	C₂²×C₃²×C₂₉	C₂²×C₃	1	39	yes	—
14	C₃²×C₄×C₂₉	C₂²×C₃	1	52	yes	direct product factor
15	C₃³×C₂₉	C₂²×C₄	1	1	yes	characteristic, direct product factor, Hall
16	C₂³×C₃×C₂₉	C₂×C₃²	1	13	yes	—
17	C₂×C₃×C₄×C₂₉	C₂×C₃²	1	78	yes	direct product factor
18	C₂×C₃²×C₂₉	C₂×C₃×C₄	1	78	yes	direct product factor
19	C₂×C₃²×C₂₉	C₂³×C₃	1	13	yes	—
20	C₂²×C₄×C₂₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₃³×C₄	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₃×C₂₉	C₃²×C₄	1	52	yes	direct product factor
23	C₂²×C₃×C₂₉	C₂²×C₃²	1	39	yes	—
24	C₃×C₄×C₂₉	C₂²×C₃²	1	52	yes	direct product factor
25	C₃²×C₂₉	C₂²×C₃×C₄	1	13	yes	direct product factor
26	C₂³×C₂₉	C₂×C₃³	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×C₃³	1	6	yes	direct product factor
28	C₂³×C₃³	C₂×C₂₉	1	1	yes	characteristic
29	C₂×C₃³×C₄	C₂×C₂₉	1	6	yes	direct product factor
30	C₂×C₃×C₂₉	C₂×C₃²×C₄	1	78	yes	direct product factor
31	C₂×C₃×C₂₉	C₂³×C₃²	1	13	yes	—
32	C₂²×C₃²×C₄	C₃×C₂₉	1	13	yes	direct product factor
33	C₂²×C₂₉	C₃³×C₄	1	4	yes	direct product factor
34	C₂²×C₂₉	C₂²×C₃³	1	3	yes	—
35	C₄×C₂₉	C₂²×C₃³	1	4	yes	direct product factor
36	C₂²×C₃³	C₄×C₂₉	1	4	yes	direct product factor
37	C₂²×C₃³	C₂²×C₂₉	1	3	yes	—
38	C₃³×C₄	C₂²×C₂₉	1	4	yes	direct product factor
39	C₃×C₂₉	C₂²×C₃²×C₄	1	13	yes	direct product factor
40	C₂³×C₃²	C₂×C₃×C₂₉	1	13	yes	—
41	C₂×C₃²×C₄	C₂×C₃×C₂₉	1	78	yes	direct product factor
42	C₂×C₂₉	C₂×C₃³×C₄	1	6	yes	direct product factor
43	C₂×C₂₉	C₂³×C₃³	1	1	yes	characteristic
44	C₂×C₃³	C₂×C₄×C₂₉	1	6	yes	direct product factor
45	C₂×C₃³	C₂³×C₂₉	1	1	yes	characteristic
46	C₂²×C₃×C₄	C₃²×C₂₉	1	13	yes	direct product factor
47	C₂²×C₃²	C₃×C₄×C₂₉	1	52	yes	direct product factor
48	C₂²×C₃²	C₂²×C₃×C₂₉	1	39	yes	—
49	C₃²×C₄	C₂²×C₃×C₂₉	1	52	yes	direct product factor
50	C₂₉	C₂²×C₃³×C₄	1	1	yes	characteristic, direct product factor, Sylow
51	C₃³	C₂²×C₄×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₂³×C₃	C₂×C₃²×C₂₉	1	13	yes	—
53	C₂×C₃×C₄	C₂×C₃²×C₂₉	1	78	yes	direct product factor
54	C₂×C₃²	C₂×C₃×C₄×C₂₉	1	78	yes	direct product factor
55	C₂×C₃²	C₂³×C₃×C₂₉	1	13	yes	—
56	C₂²×C₄	C₃³×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	C₃²×C₄×C₂₉	1	52	yes	direct product factor
58	C₂²×C₃	C₂²×C₃²×C₂₉	1	39	yes	—
59	C₃×C₄	C₂²×C₃²×C₂₉	1	52	yes	direct product factor
60	C₃²	C₂²×C₃×C₄×C₂₉	1	13	yes	direct product factor
61	C₂³	C₂×C₃³×C₂₉	1	1	yes	characteristic
62	C₂×C₄	C₂×C₃³×C₂₉	1	6	yes	direct product factor
63	C₂×C₃	C₂×C₃²×C₄×C₂₉	1	78	yes	direct product factor
64	C₂×C₃	C₂³×C₃²×C₂₉	1	13	yes	—
65	C₂²	C₃³×C₄×C₂₉	1	4	yes	direct product factor
66	C₂²	C₂²×C₃³×C₂₉	1	3	yes	—
67	C₄	C₂²×C₃³×C₂₉	1	4	yes	direct product factor
68	C₃	C₂²×C₃²×C₄×C₂₉	1	13	yes	direct product factor
69	C₂	C₂×C₃³×C₄×C₂₉	1	6	yes	direct product factor
70	C₂	C₂³×C₃³×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃³×C₂₉
socle, prime radical	C₂³×C₃³×C₂₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃³×C₄×C₂₉	C₂	direct (N × H)
3. C₂²×C₃²×C₄×C₂₉	C₃	direct (N × H)
4. C₂²×C₃³×C₂₉	C₄	direct (N × H)
6. C₃³×C₄×C₂₉	C₂²	direct (N × H)
8. C₂×C₃²×C₄×C₂₉	C₂×C₃	direct (N × H)
9. C₂×C₃³×C₂₉	C₂×C₄	direct (N × H)
11. C₂²×C₃×C₄×C₂₉	C₃²	direct (N × H)
12. C₂²×C₃²×C₂₉	C₃×C₄	direct (N × H)
14. C₃²×C₄×C₂₉	C₂²×C₃	direct (N × H)
15. C₃³×C₂₉	C₂²×C₄	direct (N × H)
17. C₂×C₃×C₄×C₂₉	C₂×C₃²	direct (N × H)
18. C₂×C₃²×C₂₉	C₂×C₃×C₄	direct (N × H)
20. C₂²×C₄×C₂₉	C₃³	direct (N × H)
21. C₂²×C₃³×C₄	C₂₉	direct (N × H)
22. C₂²×C₃×C₂₉	C₃²×C₄	direct (N × H)
24. C₃×C₄×C₂₉	C₂²×C₃²	direct (N × H)
25. C₃²×C₂₉	C₂²×C₃×C₄	direct (N × H)
27. C₂×C₄×C₂₉	C₂×C₃³	direct (N × H)
29. C₂×C₃³×C₄	C₂×C₂₉	direct (N × H)
30. C₂×C₃×C₂₉	C₂×C₃²×C₄	direct (N × H)
32. C₂²×C₃²×C₄	C₃×C₂₉	direct (N × H)
33. C₂²×C₂₉	C₃³×C₄	direct (N × H)
35. C₄×C₂₉	C₂²×C₃³	direct (N × H)
36. C₂²×C₃³	C₄×C₂₉	direct (N × H)
38. C₃³×C₄	C₂²×C₂₉	direct (N × H)
39. C₃×C₂₉	C₂²×C₃²×C₄	direct (N × H)
41. C₂×C₃²×C₄	C₂×C₃×C₂₉	direct (N × H)
42. C₂×C₂₉	C₂×C₃³×C₄	direct (N × H)
44. C₂×C₃³	C₂×C₄×C₂₉	direct (N × H)
46. C₂²×C₃×C₄	C₃²×C₂₉	direct (N × H)
47. C₂²×C₃²	C₃×C₄×C₂₉	direct (N × H)
49. C₃²×C₄	C₂²×C₃×C₂₉	direct (N × H)
50. C₂₉	C₂²×C₃³×C₄	direct (N × H)
51. C₃³	C₂²×C₄×C₂₉	direct (N × H)
53. C₂×C₃×C₄	C₂×C₃²×C₂₉	direct (N × H)
54. C₂×C₃²	C₂×C₃×C₄×C₂₉	direct (N × H)
56. C₂²×C₄	C₃³×C₂₉	direct (N × H)
57. C₂²×C₃	C₃²×C₄×C₂₉	direct (N × H)
59. C₃×C₄	C₂²×C₃²×C₂₉	direct (N × H)
60. C₃²	C₂²×C₃×C₄×C₂₉	direct (N × H)
62. C₂×C₄	C₂×C₃³×C₂₉	direct (N × H)
63. C₂×C₃	C₂×C₃²×C₄×C₂₉	direct (N × H)
65. C₂²	C₃³×C₄×C₂₉	direct (N × H)
67. C₄	C₂²×C₃³×C₂₉	direct (N × H)
68. C₃	C₂²×C₃²×C₄×C₂₉	direct (N × H)
69. C₂	C₂×C₃³×C₄×C₂₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃³×C₂₉	2
C₂×C₃³×C₄×C₂₉	2
C₂²×C₃²×C₄×C₂₉	3
C₂²×C₃³×C₄	29

Subgroups — C22×C33×C4×C29 #72190877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃³×C₄×C₂₉ #72190877